To model this using the queuing models in the chapter, assume that you have two totally independent service processes. The first process is the CSM and the second is the FPM$.$ Each process has potentially a different mean service time per customer. The CSM must serve each customer and they arrive at a particular rate. The FPM prepares the individual items on the order such as hamburgers, cheeseburgers, and fries. As the orders are taken, each individual item appears on a monitor telling the FPM what should be made next. The average time for a customer to run through the system is the sum of the average service times $($time to take the order by the CSM and time to make the order by the FPM$)$ plus the sum of the expected waiting times for the two processes. This assumes that these processes operate totally independent of each other, which might not be exactly true. But we leave that to a later discussion.

Assume that the queues in front of each process are large, meaning that there is plenty of room for cars in the line before and after the order kiosk. Also, assume there is a single CSM and two FPMs each operating independently and working just on the drive$-$through orders. Also, assume that the arrival pattern is Poisson, customers are handled first come, first served, and the service pattern is exponential.

Consider a base case where a customer arrives every $40$ seconds and the Customer Service Manager can handle $120$ customers per hour. There are two Food Preparation Managers, each capable of handling $100$ orders per hour.

Currently, relatively few customers $($less than $(1)/(2)$ percent$)$ order the Onion Hamburger Deluxe. What would happen if the restaurant ran a sale on Onion Hamburger Deluxe, so that the customer arrival rate increased by $20\%,$ and $30\%$ of the orders were now for this item? Assume that the Customer Service Manager never helps the Food Preparation Manager and that these two processes remain independent. Use Exhibit $10\mathrm{.}9.$